The Queen’s granddaughter Zara Phillips and her rugby player husband, Mike Tindall, are expecting their first child.

Phillips, daughter of the Princess Royal and her first husband, Captain Mark Phillips, is due to give birth in the new year.

In a statement Buckingham Palace said: “Mr and Mrs Mike Tindall are very pleased to announce that Zara Tindall is expecting a baby in the new year.

“The Princess Royal and Captain Mark Phillips, Mr Phillip and Mrs Linda Tindall, and members of both families are delighted with the news.

“This baby will be the first child for Mike and Zara and the third grandchild for the Princess Royal.”

Zara, 32, will be 15th in line to the throne after the Duchess of Cambridge gives birth to her baby, which is due in mid-July.

David Cameron’s official spokesman described the announcement as “quite terrific news” saying: “The prime minister will send his very, very best wishes to the happy couple.”

Phillips – she still uses her maiden name in her equestrian career – was a member of the British eventing team at the London Olympics and won a silver medal which was presented to her by her mother, Princess Anne.

Tindall, 34, whom she married in July 2011, is a former England captain who plays for Gloucester.

They have talked openly about their desire to begin a family but the couple’s sporting commitments, particularly in the runup to the Olympics, meant their schedules were hectic.

Launching his charity Rugby for Heroes in May 2012, Tindall said: “Obviously we’re going to have a family. But it’s about timing.” He added then: “I want to play for another two years, so it’s just where we find the balance in that. I wouldn’t say we’ll wait; we’ll try and find a window.”

The couple, who met at the 2003 Rugby World Cup in Australia, were married in Edinburgh’s Canongate Kirk in a private ceremony attended by all the senior members of the royal family three months after the wedding of the Duke and Duchess of Cambridge.

Just months later Tindall was fined and booted out of the England rugby squad for drunken antics during the World Cup in New Zealand. He was reportedly seen embracing an ex-girlfriend, and alleged to have attended an event with fellow players – “the Mad Midget Weekender” – which was said to have featured a “dwarf-tossing” competition, though the manager of the bar in Queenstown later denied that any dwarf-throwing had taken place at the event.

Tindall was later reinstated to the team and had his fine reduced because he could not remember the drinking session and did not intentionally mislead the RFU team management.

The baby will be a fourth great-grandchild for the Queen. Like Zara and her brother Peter Phillips, it will not hold a royal title or the style HRH. Peter Phillips, 35, the Queen’s eldest grandchild, and his wife, Autumn, a Canadian management consultant who converted from Catholicism to marry him, have two daughters, Savannah, aged two and a half, and Isla, aged one.